A stone is projected at an angle `alpha` to the horizontal from the top of a tower of height 3h. If the stone reaches a maximum height 'h', above the tower, show that it reaches the ground at a distance 6h cot `alpha` from the foot of the lower.

Explanation

Total time to reach the ground
=time to reach the highest point, i.e., a height 'h'
above the tower+the time to falls freely from a height 4h to the ground
`=(u sin alpha)/(g)+sqrt((2(rh))/(g))=sqrt((2h)/(g))+sqrt(8h)/(g)`
`=3xxsqrt((2h)/(g)) (because(u^(2)sin^(2)alpha)/(2g)=h)`
During this time, the distance travelled horizontally =timexx horizontal velocity
`=3sqrt((2h)/(g))xxu cos alpha=3sqrt((2h)/(g))sqrt((2gh)/(sin^(2)alpha))cos alpha`